WBJEE · Maths · Application of Derivatives
If \(x=-1\) and \(x=2\) are extreme points of \(f(x)=\alpha \log |x|+\beta x^2+x,(x \neq 0)\), then
- A \(\alpha=-6, \beta=\frac{1}{2}\)
- B \(\alpha=-6, \beta=-\frac{1}{2}\)
- C \(\alpha=2, \beta=-\frac{1}{2}\)
- D \(\alpha=2, \beta=\frac{1}{2}\)
Answer & Solution
Correct Answer
(C) \(\alpha=2, \beta=-\frac{1}{2}\)
Step-by-step Solution
Detailed explanation
\(f^{\prime}(x)=\frac{\alpha}{|x|} \cdot \frac{|x|}{x}+2 \beta x+1, f(-1)=f(2)=0\) So, \(-\alpha-2 \beta+1=0 \Rightarrow \alpha+2 \beta-1=0\) ...(i) \(\& \frac{\alpha}{2}+4 \beta+1=0 \Rightarrow \alpha+8 \beta+2=0\)....(ii) (ii) - (i)…
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